Fracturing a subsurface formation based on the required breakdown pressure

Abstract

Some methods of hydraulic fracturing of a subsurface formation include using a three-dimensional finite element model to simulate a deviated well with a wellbore casing, a cement adjacent to the wellbore casing, and a perforation cluster with at least two perforations. The FEM is applied (or solved) to determine a breakdown pressure of the deviated well based on an amount of tensile damage of the perforation cluster induced by an applied pressure representing injected hydraulic fluid. The FEM accounts for the 3D complex configuration of wellbore and perforation cluster. A deviated well is drilled and completed with a wellbore casing size, tubing size, wellhead, and hydraulic fracturing pump schedule selected at least in part based on the determined breakdown pressure before hydraulic fluid is injected into the deviated well at an injection pressure, which represents the required breakdown pressure to cause hydraulic fracturing of the rock of the subsurface formation.

What is claimed is: 
     
       1. A method of hydraulic fracturing a subsurface formation, the method comprising:
 using a three-dimensional finite element model implemented on one or more processors to simulate a deviated well with a wellbore casing, a cement adjacent to the wellbore casing, and a perforation cluster with at least two perforations through a side wall of the wellbore casing, each of the at least two perforations extending through a rock of the subsurface formation via a respective perforation tunnel and having a different phase angle relative to an longitudinal axis of the casing; 
 solving the three-dimensional finite element model implemented on one or more processors to determine a breakdown pressure of the deviated well based on an amount of tensile damage of the perforation cluster induced by an applied pressure representing injected hydraulic fluid; 
 drilling and completing a deviated well with a wellbore casing size, tubing size, and wellhead selected at least in part based on the determined breakdown pressure; and 
 injecting hydraulic fluid into the deviated well at an injection pressure determined at least in part on the determined breakdown pressure to cause hydraulic fracturing of the rock of the subsurface formation, 
 wherein the three-dimensional finite element model includes a concrete damage plasticity model representing constitutive behavior of the rock and a contact relationship between an interface of the wellbore casing and the cement adjacent to the casing, the contact relationship modeling de-bonding of the interface of the casing and the cement. 
 
     
     
       2. The method of  claim 1 , further comprising extracting material properties of the rock from log data and/or lab test data, wherein the concrete damage plasticity model includes compression hardening, compression damage, tensile stiffening, and tensile damage behavior at least in part based on the extracted material properties. 
     
     
       3. The method of  claim 1 , wherein injecting hydraulic fluid into the deviated well comprises pumping the hydraulic fluid into the deviated well using a hydraulic fracturing pump schedule determined at least in part based on the determined breakdown pressure. 
     
     
       4. The method of  claim 1 , wherein each of the at least two perforations are axially spaced relative to each other and each of the at least two perforations are angularly spaced relative to each other around a circumference of the wellbore. 
     
     
       5. The method of  claim 4 , wherein the at least two perforations are six perforations located within a 20 centimeter length of the wellbore casing and angularly spaced 60 degrees apart. 
     
     
       6. The method of  claim 1 , wherein determining the breakdown pressure comprises detecting when at least one finite element representing the rock has a tensile failure above a predetermined threshold. 
     
     
       7. The method of  claim 6 , wherein the predetermined threshold is a scalar between 0.0 and 0.2. 
     
     
       8. The method of  claim 1 , wherein solving the three-dimensional finite element model comprises solving the three-dimensional finite element model using two quasi-static loading steps, a first step used for solving static equilibrium with a loading of in-situ stresses, gravity loading, overburden, and underburden, and a second step used for solving static equilibrium of an applied pressure to determine the breakdown pressure while including the loading of the first step. 
     
     
       9. The method of  claim 1 , further comprising rotating an orientation of the three-dimensional finite element model based on borehole image log data so that a well trajectory orientation and in-situ stresses are oriented in accordance with the borehole image log data. 
     
     
       10. A method of hydraulic fracturing a subsurface formation, the method comprising:
 implementing a three-dimensional finite element model on one or more processors to simulate a deviated well with a wellbore casing, a cement adjacent to the wellbore casing, and a perforation cluster with at least two perforations through a side wall of the wellbore casing, each of the at least two perforations extending through a rock of the subsurface formation via a respective perforation tunnel and having a different phase angle relative to an longitudinal axis of the casing; 
 assigning a concrete damage plasticity model to define constitutive behavior of the rock of the subsurface formation, the concrete damage plasticity model including compression hardening, compression damage, tensile stiffening, and tensile damage behavior; 
 assigning a contact relationship at an interface between the casing and the cement, the contact relationship modeling de-bonding of the interface between the casing and the cement; and 
 solving the three-dimensional finite element model on the one or more processors to determine a breakdown pressure of the deviated well based on an amount of tensile damage of the rock induced by an applied pressure representing injected hydraulic fluid and the assigned concrete damage plasticity model and the assigned contact relationship. 
 
     
     
       11. The method of  claim 10 , further comprising extracting material properties of the rock from log data and/or lab test data, wherein the compression hardening, compression damage, tensile stiffening, and tensile damage behavior of the concrete damage plasticity model of the rock are at least in part based on the extracted material properties. 
     
     
       12. The method of  claim 10 , further comprising rotating an orientation of the three-dimensional finite element model based on borehole image log data so that a well trajectory orientation and in-situ stresses are oriented in accordance with the borehole image log data. 
     
     
       13. The method of  claim 10 , wherein each of the at least two perforations are axially spaced relative to each other and angularly spaced relative to each other around a circumference of the wellbore. 
     
     
       14. The method of  claim 13 , wherein the at least two perforations are six perforations located within a 20 centimeter length of the wellbore casing and angularly spaced 60 degrees apart. 
     
     
       15. The method of  claim 10 , wherein an output of the solved three-dimensional finite element model is a spatially varying contour of the tensile damage of the rock. 
     
     
       16. The method of  claim 10 , wherein determining the breakdown pressure comprises detecting when at least one finite element representing the rock has a tensile failure above a predetermined threshold. 
     
     
       17. The method of  claim 16 , wherein the predetermined threshold is a scalar between 0.0 and 0.2. 
     
     
       18. The method of  claim 10 , wherein a portion of the deviated well has a deviated angle of at least 10 degrees relative to a normal direction from a ground surface. 
     
     
       19. The method of  claim 10 , further comprising selecting a wellbore casing size, a tubing size, and wellhead at least in part based on the determined breakdown pressure. 
     
     
       20. The method of  claim 19 , further comprising determining a hydraulic fracturing pump schedule for injecting hydraulic fluid into the wellbore at least in part based on the determined breakdown pressure.